With the match heading towards a penalty shootout, Dutch coach Louis van Gaal brought Krul on for Cillessen in the final minute of extra time.
The Newcastle United stopper went on to make two saves in the shootout to send his country into the semi-finals.
Cillessen has revealed that he kicked a water bottle at teammate Bruno Martins Indi as he came off the field.
"I didn't know it would happen before, it was a bit of a surprise. I was a bit angry. I wanted to play the penalty shootout," Cillessen told BBC Sport.
"I was angry, and went out. I kicked the water bottle - Bruno was feeling warm so I did it to cool him down. It is a pity I wasn't told, but it worked very well. He made two saves."
Netherlands will face Argentina in the last four on Wednesday.